Basic radio theory, circuits and calculations

The decibel notation

The need to compare voltage levels or power levels at different points in a circuit or at different frequencies very often arises in radio engineering.

The most realistic way to do this is by means of the decibel notation which is based on logarithms as the following example shows.

Consider the statement 'the power level has increased by 1W. ' What does this mean? Obviously an increase in power from 0.25W to 1.25W is vastly different from an increase from 10W to 11W or from 100W to 101W, yet in each case the power level has increased by only 1W.

Table 2.3. Ratios of power and voltage In terms of decibels

dB	Power ratio	Voltage ratio	dB	Power ratio	Voltage ratio
1	1.26	1.12	15	31.6	5.62
2	1.58	1.26	20	100	10
3	2.00	1.41	30	1000	31.6
4	2.51	1.58	40	10⁴	10²
5	3.16	1.78	50	10⁵	316
6	3.98	2.00	60	10⁶	10³
7	5.01	2.24	70	10⁷	3160
8	6.31	2.51	80	10⁸	10⁴
9	7.94	2.82	90	10⁹	31600
10	10.00	3.16	100	10¹⁰	10⁵

The effect of a 1W increase in power in each case may be compared with the use of the decibel notation. The difference between a power level W₁, and a power level W₂ when expressed in decibels is:

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In the above examples

(a) 0.25W to 1.25W $images\x11-2.gif$
(b) 10W to11W $images\x11-3.gif$
(c) 100W to 101W $images\x11-4.gif$

The advantage of this notation is therefore obvious. Voltages may also be compared in this way, since:

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Other ratios may be calculated easily from the above. If two decibel figures are added, the corresponding power or voltage ratios must be multiplied, eg

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The decibel notation is a way of expressing a ratio, therefore it can only be used to express a magnitude when a reference level is defined. This is often done as follows.

The unit 'dBW' specifies a power level which is so many decibels above one watt, ie the reference level. Thus +20dBW is a power level which is 20dB above one watt, ie 100 watts. The + sign here is quite often omitted. (Note 0dBW is zero dB above 1 watt. ie it is 1 watt')

This is the method now used to express transmitter output power in the UK amateur radio licence.

Powers less than 1 watt are also expressed in this way, eg -20dBW means 20dB down on 1 watt, that is 10mW (the negative sign here is never omitted). Similarly, 20dBmW is 20dB up on 1mW or 100mW. And -20dBmW is 20dB below 1mW, that is 10nW.

Other common examples of the use of the decibel are:

(a) The variation in gain of an audio amplifier at different frequencies may be expressed as so many decibels above or below the gain at, say, 1000Hz.
(b) The characteristic of a bandpass filter is specified by its shape factor which is the ratio of its bandwidths at -60dB and -6dB.
(c) The variation in level of the selectivity or response curve of a tuned circuit or receiver is expressed in decibels (see Fig 5.6).
(d) The AGC characteristic of a receiver is a graph of the variation in output of the receiver (in decibels) plotted against increasing signal input (also in decibels).

Other reference levels used are 'dBV' and 'dBmV'. 'dBd' and 'dBi' are used to compare the gain of an antenna with reference to a dipole or an isotropic radiator respectively.

Note: 'dBmW' is commonly abbreviated to 'dBm'.

Acoustic power level (ie loudness) is also specified in decibels, a standard reference level being assumed.

A useful series of Decibel calculators

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